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A349274 Decimal expansion of the arc length of the logarithmic spiral related to a golden triangle with a unit base length. 1
4, 9, 2, 5, 1, 7, 5, 4, 3, 9, 4, 7, 8, 0, 5, 8, 8, 3, 7, 1, 9, 3, 1, 7, 6, 0, 4, 6, 8, 1, 3, 5, 6, 5, 6, 7, 4, 2, 2, 4, 5, 7, 0, 1, 9, 2, 8, 4, 0, 6, 9, 5, 2, 2, 2, 1, 5, 2, 0, 5, 8, 0, 2, 2, 0, 9, 4, 6, 3, 2, 5, 2, 4, 4, 3, 4, 6, 5, 2, 2, 6, 3, 3, 9, 0, 1, 5, 4, 3, 1, 5, 2, 0, 7, 8, 4, 4, 6, 8, 9, 5, 8, 3, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The spiral starts at the triangle's apex (the vertex opposite to the base) and converges to the pole (the accumulation point).
REFERENCES
H. E. Huntley, The Divine Proportion: A Study in Mathematical Beauty, New York: Dover Publications Inc., 1970, pp. 170-176.
Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number, New York: Broadway Books, 2002, p. 119.
LINKS
Eric Weisstein's World of Mathematics, Golden Triangle.
Eric Weisstein's World of Mathematics, Logarithmic Spiral.
Wikipedia, Logarithmic spiral.
FORMULA
Equals sqrt((17 + 7*sqrt(5))/22) * sqrt(1 + b^2)/b, where b = 5*log(phi)/(3*Pi), and phi = (1+sqrt(5))/2 is the golden ratio (A001622).
EXAMPLE
4.92517543947805883719317604681356567422457019284069...
MATHEMATICA
b = 5 * Log[GoldenRatio]/(3*Pi); RealDigits[Sqrt[(17 + 7*Sqrt[5])/22] * Sqrt[1 + b^2]/b, 10, 100][[1]]
CROSSREFS
Sequence in context: A254159 A125575 A199725 * A021071 A197146 A021207
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Nov 12 2021
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)